Nonlinear Analysis of Fluid Problem with Free Surface by High-Speed Visual Processing System

本文将贮库结构中流体的非线性晃动问题作为本文标题中提到的有自由表面的非线性流体问题来处理。在理论处理中，基于变分原理和积分方程的数值方法被处理，其中研究了旋转现象以及自由表面具有有限振幅的通常晃动现象。本文采用圆柱形和球形两种贮箱模型进行了地震振动台试验，并成功地利用了新引进的高速视觉处理系统。对于贮液器内流体的非线性响应：1）频率在线性共振域附近的外激励容易引起贮液器内流体的有限幅非线性晃动响应，其结果是贮液器壁面动压力的非线性效应变得非常大，在贮液器结构设计中不可忽略; 2）旋流现象可以描述为晃动响应的动力分量与垂直于外激励方向的动力分量之间的非线性分叉现象。对于数字视觉处理系统：1）从高速视频系统获得的视觉数据可以通过本图像处理单元生动地数字化，因此本目标不需要如此昂贵的超高分辨率系统。2）使用网格投影技术获得的数字化数据足够精细，可以恢复变形自由表面的原始三维数据。

Present report deals with the nonlinear sloshing of the fluid in the storage structures as the nonlinear fluid problem with free surface mentioned in the title of this report. In the theoretical treatment, numerical approaches based on both the variational principle and the integral equation are dealt with, where swirling phenomena investigated as well as usual sloshing phenomena with finite amplitude of the free surface. Experimental insurance by using the shaking table test are carried out, where the cylindrical and the spherical storage model are used and newly introduced High-Speed Visual Processing System has been successfully utilized.Results obtained by the theoretical and experimental research mentioned above can be summarized as follows. For the nonlinear responses of the fluid in the storages:1) the nonlinear sloshing responses with finite amplitude can be easily caused by the external excitation with the frequency in the neighborhood of the linear resonance domain and, as the results, the nonlinear effect of the dynamic pressure on the wall of the storage becomes so large that one can not ignore in the structural design of the liquid storage.2) swirling phenomenon can be described as the nonlinear bifurcational phenomenon between the dynamic component of the sloshing response and that in the durection perpendicular to one of the external excitation. For the digital visual processing system:1) visual data obtained from the high-speed video system can be vividly digitized by the present image processing unit that such an expensive system with super-high resolution system is not required for the present objective.2) digitized data obtained by using the grid-projection technique are sufficiently fine for restoration of the original three dimensional data for the deformed free surface.